Recall that a subobject \(U \subset X\)  is open if the associated map \(\mathrm {Sh}(\mathcal {C}_U) \rightarrow \mathrm {Sh}(\mathcal {C})\)  is an open immersion of topoi, cf. [1]} for the latter notion. Note that unlike the unbounded gluing results proved in [2]} or [1]}, we do not assume here that the underlying site locally has finite cohomological dimension. The price to pay is that we only prove gluing for open covers.
